To find out how many meters the airplane can ascend in 1 second, we need to first express the rate of ascent in a simpler form.
The airplane ascends at a rate of \( 51 \frac{1}{2} \) meters in \( \frac{2}{3} \) of a second. First, we convert \( 51 \frac{1}{2} \) to an improper fraction:
\[ 51 \frac{1}{2} = 51 + \frac{1}{2} = \frac{102}{2} + \frac{1}{2} = \frac{103}{2} \text{ meters} \]
Now, we know the airplane ascends \( \frac{103}{2} \) meters in \( \frac{2}{3} \) seconds. To find the ascent in 1 second, we can set up a proportion:
\[ \text{Ascend in 1 second} = \left(\frac{103}{2} \text{ meters}\right) \div \left(\frac{2}{3} \text{ seconds}\right) \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{103}{2} \times \frac{3}{2} = \frac{103 \times 3}{2 \times 2} = \frac{309}{4} \text{ meters} \]
Now, we can convert \( \frac{309}{4} \) back to a decimal:
\[ \frac{309}{4} = 77.25 \text{ meters} \]
Therefore, the airplane can ascend 77.25 meters in 1 second.